This junior/senior level course in classical Euclidean geometry from a
contemporary viewpoint is woven from five threads
1. The Physical Origins of Greek Geometry.
2. Renaissance Perspective and 3-dimensional Drawing.
3. The Industrial Origins of Cartesian Geometry.
4. Klein's Erlangen Program to Unify Geometry.
5. The Geometry in Computer Graphics.
The initial 3 week unit on affine Geometry, including the theorems of Ceva, Menelaus, Desargues and Pappus is a good review of Euclidean plane geometry but using vector methods. There follows a 4-week unit on the practice and theory of perspective drawing which serves as an introduction to visualizing 3-dimensions and to classical projective geometry. A 2 week unit on dilatations, applied to constructing Euler's line and the Nine-point circle, introduces transformational geometry. Klein's Erlangen Program, defining geometries in terms of their isometry groups, and the classification of isometries (congruences) in the Euclidean plane occupies remaining 6 weeks of the course.
There will be weekly graded assignments, including homework submitted online, and written in LaTeX. The first test is M5, the midterm is M8, the takehome test is F10-F11, and the third test is W14. The 3 hr written final is at the prescribed time (Noncombined List) 8am Tuesday, 13dec11. Please resolve conflicts early in the semester and do not schedule absences on announced test dates. The course grade assesses the student's final comprehension and achievement in the course, not a statistical accumulation of points. The traditional average grade for the course is 3.2 based on a weighted average of 30% for the 3hr written final, 40% tests (10% each), and 30% for class participation, homework, quizzes.
This course satisfies requirements in several math and education curricula. Since MA402 also treats non-Euclidean geometry (affine, projective) it qualifies for the Illinois Certification Testing System, Field 115: Mathematics, November 2003, requirement. The course can also be taken as a technical elective in science and engineering. Its strong emphasis on visual comprehension and its historical flavor makes it accessible to students in the fine and applied arts. The course may be taken for 3 or 4 credit hours.
The unit on perspective will include an opportunity for doing a substantial visual project for those students taking the course for 4 credit hours. Such a project is equivalent to a term paper but may consist of a well documented drawing, model construction, computer animation, video etc. The form and content is open to negotiation, and it is adapted to the interest and skill of the student. The project requires a proposal, progress report and 4-6 pages of written documentation in LaTeX. Drafts of this documentation will be returned for correction. The additional credit hour is available for this project.
The 3 credit version does not require the substantial project on perspective with full documentation. But a project may nevertheless be completed for extra credit and/or makeup for missed assignments.
The prerequisites for the course are Calculus III (MA241 or its equivalent) for the use of vectors, and MA347 or its equivalent for the maturity in understanding and writing rigorous proofs gained there. Consent of the instructor may be obtained on the basis of some other, substantial experience with mathematical proofs.
Keeping a handwritten journal as specified is a requirement. You are encouraged to participate in mathematically meaningful activities such as seminars, films, exhibits, cultural events etc. Reports on such activities may be used to make up missed assignments.
Summary of Student Class Evaluation of the course in 2012.
Summary of Student Class Evaluation of the course in 2010.
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